I believe the work has temporarily stopped because the next stage (adding panelling to the central section) requires some coordination with Skanska to install new lighting at the same time, and is most likely to result in the subway being closed for more than a few hours at a time.
The new floor and the painting of the walls that are not to be clad, had to be done in advance for the best finish. I did recently ask for an update from Lewisham council transport liaison meeting, but I ended up giving the update (regarding the lack of visible progress) rather than representatives from Lewisham, LOROL, and Network Rail.